{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "03473fbd-7f0c-4ece-9639-ed73a7c33aba",
   "metadata": {},
   "source": [
    "# Approximated State Preparation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "475ba3de-99df-4be9-b327-fe6d5e79a8fb",
   "metadata": {},
   "source": [
    "This tutorial demonstrates an approximated quantum function: a state preparation. Depending on the given functional error, the synthesis engine automatically chooses implementation with fewer resources. The demonstration is on a random state vector, of size $2^6$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b0914a0f-115e-4593-8f78-8694126f3e14",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T14:00:37.680386Z",
     "iopub.status.busy": "2024-05-07T14:00:37.680138Z",
     "iopub.status.idle": "2024-05-07T14:00:37.773087Z",
     "shell.execute_reply": "2024-05-07T14:00:37.772439Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "NUM_QUBITS = 6\n",
    "np.random.seed(12)\n",
    "amplitudes = 1 - 2 * np.random.rand(2**NUM_QUBITS)\n",
    "amplitudes = (amplitudes / np.linalg.norm(amplitudes)).tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a5f845ce-ea00-4e73-979d-22a037f45e0e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T14:00:37.782871Z",
     "iopub.status.busy": "2024-05-07T14:00:37.776482Z",
     "iopub.status.idle": "2024-05-07T14:00:37.789516Z",
     "shell.execute_reply": "2024-05-07T14:00:37.788815Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The upper bounds: [0.         0.03333333 0.06666667 0.1        0.13333333 0.16666667\n",
      " 0.2        0.23333333 0.26666667 0.3       ]\n"
     ]
    }
   ],
   "source": [
    "bounds = np.linspace(0.0, 0.3, 10)\n",
    "print(\"The upper bounds:\", bounds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6b9a9dbb-e730-44f8-8dc8-db51266c727f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T14:00:37.794404Z",
     "iopub.status.busy": "2024-05-07T14:00:37.793058Z",
     "iopub.status.idle": "2024-05-07T14:09:45.222086Z",
     "shell.execute_reply": "2024-05-07T14:09:45.221250Z"
    }
   },
   "outputs": [],
   "source": [
    "from classiq import (\n",
    "    Constraints,\n",
    "    CustomHardwareSettings,\n",
    "    OptimizationParameter,\n",
    "    Preferences,\n",
    "    QArray,\n",
    "    QuantumProgram,\n",
    "    create_model,\n",
    "    prepare_amplitudes,\n",
    "    qfunc,\n",
    "    set_constraints,\n",
    "    set_preferences,\n",
    "    show,\n",
    "    synthesize,\n",
    ")\n",
    "\n",
    "preferences = Preferences(\n",
    "    custom_hardware_settings=CustomHardwareSettings(basis_gates=[\"cx\", \"u\"]),\n",
    "    random_seed=1235,\n",
    "    optimization_timeout_seconds=100,\n",
    "    transpilation_option=\"custom\",\n",
    ")\n",
    "\n",
    "\n",
    "depths = []\n",
    "cx_counts = []\n",
    "\n",
    "\n",
    "for b in bounds:\n",
    "\n",
    "    @qfunc\n",
    "    def main() -> None:\n",
    "        out = QArray(\"out\")\n",
    "        prepare_amplitudes(amplitudes=amplitudes, bound=b, out=out)\n",
    "\n",
    "    qmod = create_model(main)\n",
    "    qmod = set_preferences(qmod, preferences)\n",
    "    qprog = synthesize(qmod)\n",
    "\n",
    "    circuit = QuantumProgram.from_qprog(qprog)\n",
    "    depths.append(circuit.transpiled_circuit.depth)\n",
    "    cx_counts.append(circuit.transpiled_circuit.count_ops[\"cx\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c560f667-7bf0-4282-b258-9a87e5db485e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T14:09:45.227778Z",
     "iopub.status.busy": "2024-05-07T14:09:45.226254Z",
     "iopub.status.idle": "2024-05-07T14:09:45.233599Z",
     "shell.execute_reply": "2024-05-07T14:09:45.232860Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "classiq depths: [9874, 8721, 8259, 7908, 7677, 7447, 6986, 6755, 6525, 6295]\n",
      "cx-counts depths: [6548, 5748, 5428, 5196, 5036, 4876, 4556, 4396, 4236, 4076]\n"
     ]
    }
   ],
   "source": [
    "print(\"classiq depths:\", depths)\n",
    "print(\"cx-counts depths:\", cx_counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9f67d9f0-47b5-4064-936e-3a5271949e8c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T14:09:45.238258Z",
     "iopub.status.busy": "2024-05-07T14:09:45.237036Z",
     "iopub.status.idle": "2024-05-07T14:09:45.653930Z",
     "shell.execute_reply": "2024-05-07T14:09:45.653169Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-0.05,  0.  ,  0.05,  0.1 ,  0.15,  0.2 ,  0.25,  0.3 ,  0.35]),\n",
       " [Text(-0.05, 0, '\u22120.05'),\n",
       "  Text(0.0, 0, '0.00'),\n",
       "  Text(0.05, 0, '0.05'),\n",
       "  Text(0.10000000000000002, 0, '0.10'),\n",
       "  Text(0.15000000000000002, 0, '0.15'),\n",
       "  Text(0.2, 0, '0.20'),\n",
       "  Text(0.25000000000000006, 0, '0.25'),\n",
       "  Text(0.30000000000000004, 0, '0.30'),\n",
       "  Text(0.35000000000000003, 0, '0.35')])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "classiq_color = \"#D7F75B\"\n",
    "plt.rcParams[\"font.family\"] = \"serif\"\n",
    "plt.rc(\"savefig\", dpi=300)\n",
    "\n",
    "plt.rcParams[\"axes.linewidth\"] = 1\n",
    "plt.rcParams[\"xtick.major.size\"] = 5\n",
    "plt.rcParams[\"xtick.minor.size\"] = 5\n",
    "plt.rcParams[\"ytick.major.size\"] = 5\n",
    "plt.rcParams[\"ytick.minor.size\"] = 5\n",
    "\n",
    "\n",
    "plt.plot(\n",
    "    np.round(bounds, 2),\n",
    "    depths,\n",
    "    \"o\",\n",
    "    label=\"classiq depth\",\n",
    "    markerfacecolor=classiq_color,\n",
    "    markeredgecolor=\"k\",\n",
    "    markersize=8,\n",
    "    markeredgewidth=1.5,\n",
    ")\n",
    "plt.plot(\n",
    "    np.round(bounds, 2),\n",
    "    cx_counts,\n",
    "    \"*\",\n",
    "    label=\"classiq cx-counts\",\n",
    "    markerfacecolor=classiq_color,\n",
    "    markeredgecolor=\"k\",\n",
    "    markersize=12,\n",
    "    markeredgewidth=1.5,\n",
    ")\n",
    "\n",
    "\n",
    "plt.legend(fontsize=16, loc=\"upper right\")\n",
    "\n",
    "\n",
    "plt.ylabel(\"Depth, CX-count\", fontsize=16)\n",
    "plt.xlabel(\"error bound ($L_2$ metric)\", fontsize=16)\n",
    "plt.yticks(fontsize=16)\n",
    "plt.xticks(fontsize=16)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
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